Porous rocks are saturated with fluids. The fluids may be water, gas, or oil, or a mixture of all three. The flow of current in the earth is determined by the resistivities of such rocks, which are affected by the saturating fluids. For instance, brine-saturated porous rocks are much less resistive than the same rocks filled with hydrocarbons. Hence, the geophysical objective is to determine whether hydrocarbons are present by measuring the resistivity of geological formations. If tests using other methods, for instance seismic exploration, suggest that a geological formation has the potential to bear hydrocarbons, then before drilling it is important to have some indication as to whether the formation does in fact contain hydrocarbons or whether it is primarily water bearing. This can be done using electromagnetic techniques, and more specifically time domain electromagnetic techniques.
For nearly a century direct current (DC) methods have been used on the earth's surface to determine subsurface resistivity distributions. The earliest work was by the Schlumberger brothers and by Wenner (Wenner, F., 1912, A method for measuring earth resistivity. US Bureau of Standards Bulletin, 12,469-478.). There are three general DC resistivity surveying methods: vertical electrical soundings (VES), profiling, and imaging. In VES surveys the dimensions of a selected measurement array increase whilst the central point of the array remains fixed. As the array expands, currents penetrate deeper and the resulting sounding curves are interpreted as resistivity changes with depth. In profiling surveys both the array type and its dimensions are selected for a particular depth of investigation. The array is moved along the surface to determine lateral variations of resistivity. The imaging, or earth resistance tomography (ERT) method, combines VES and profiling. In this, a large number of electrodes are placed in the ground, usually equally spaced, and are connected with a multi-core cable to a resistivity meter. The system operates under software control where any two electrodes may be selected as current electrodes, and any two others may be selected as potential (voltage) electrodes. Resistivity values are obtained on a cross section beneath the profile and indicate both lateral and depth variations.
DC measurements are made by injecting direct current between two source electrodes S1 and S2 and measuring the voltage between two receiver electrodes R1 and R2. From the current I injected at the source electrodes and voltage V measured at the receiver electrodes, a value of the apparent earth resistance is obtained by Ohm's law:Rapp=V/I Ohm  (1)
An apparent value of the subsurface resistivity ρapp can be obtained from this resistance asρapp=kRapp Ohm m  (2)in which k has units of metres and is a geometric factor that depends on the arrangement of the four electrodes. Using this apparent resistivity, the true sub-surface resistivity can be determined. A good review of techniques for determining the true value of the subsurface resistivity distribution from the apparent resistivity values is given by Loke M. H., 1999, in Electrical imaging surveys for environmental and engineering studies (http://www.abem.com/fip/Loke/2Dnotes.pdf).
There are several well-known configurations of the four electrodes for DC measurements, three of which are illustrated in FIGS. 1 to 3. FIG. 1 shows the Wenner array, FIG. 2 shows the Schlumberger array, and FIG. 3 shows the dipole-dipole array. For each array there is a different k factor, as given below
                                          k            WENNER                    =                      2            ⁢            π            ⁢                                                  ⁢            a                          ,                            (        3        )                                                      k            SCHLUMBERGER                    =                                                    2                ⁢                π                ⁢                                                                  ⁢                                  a                  2                                            b                        ⁡                          [                              1                -                                                      b                    2                                                        4                    ⁢                                          a                      2                                                                                  ]                                      ,                              for            ⁢                                                  ⁢            a                    ≥                      5            ⁢            b                          ,                            (        4        )                                          k                      DIPOLE            -            DIPOLE                          =                  π          ⁢                                          ⁢                      an            ⁡                          (                              n                +                1                            )                                ⁢                                    (                              n                +                2                            )                        .                                              (        5        )            
The dipole-dipole array of FIG. 3 determines lateral resistivity variations better than depth variations. The potential difference to be measured between the potential electrodes decays with the cube of the distance from the current electrodes. This has restricted the configuration of the array for practical purposes to values of n≦6. Edwards (Edwards, L. S., 1977, A modified pseudosection for resistivity and IP. Geophysics, 42, 1020-1036) discussed the presentation of pseudo-sections for resistivity and IP specifically for the dipole-dipole array. Theory and practical results are presented for n≦6 and reference is made to an “ideal array” with n=∞.
As shown in FIG. 5, the depth of investigation d is related to the dipole lengths a and the dipole separation na. In this case, the maximum depth of investigation d for which the earth's resistivity can be inferred is related to the configuration and is of the order of (n+2)a/5. In practice, since the signal amplitude at the receivers decreases approximately as (na)−3, while the noise level is independent of n and a, the signal-to-noise ratio decreases as (na)−3. The signal level can be increased by increasing the current injected at the source and by increasing the dipole distance a. With the levels of current that can be safely injected into the ground, the n is normally not greater than about 6, and it follows thatd≦1.6a  (6)
In other words, the depth of investigation d is less than 1.6 times the separation a between source or receiver electrodes. Increasing a increases the depth of investigation but reduces the resolution of the mapped subsurface resistivity distribution.
When making DC measurements, it has been found that the electrodes become polarised if the current is the same polarity for a long time and a false measurement of the voltage in the earth between R1 and R2 is obtained. Two strategies are used to overcome this problem. One is to use non-polarising electrodes. The other, more popular, approach is to switch the polarity of the DC current periodically; this in fact gives an alternating square-wave input current, or AC. All modern equipment uses this technique.
In the AC approach variations can be introduced, such as switching the current to zero for certain periods, for instance as shown in FIG. 4. In this case, the period T between switches is typically of the order of 1 second. The function shown here repeats every 4T. In the periods that the current is switched on between source electrodes S1 and S2, an estimate of the resulting DC voltage between R1 and R2 is made. In fact, the voltage between R1 and R2 is not exactly constant in these periods: the signal takes some time to reach a steady-state value and there is noise. To compensate for the noise various averaging techniques are used. It should be noted that in this context the term ‘DC’ in ‘DC resistivity’ means essentially low frequency, rather than zero frequency. This is already accepted in the geophysical exploration industry.
Every time the current at the source electrodes is switched, the earth responds and the voltage at the receiver electrodes changes. The flow of current in the ground is governed by the diffusion equation and it takes time for the response at the receiver to reach a steady state. This is well known, and the estimate of the DC level is measured in a time interval towards the end of the period that the current is switched on. For example, the Geopulse Tigre Resistivity Meter uses voltage measurements that are made during the latter 4/5 of the on period of the current (User's Manual, Geopulse Resisitivity Meter, Campus International Products Limited, Concept House, 8 The Townsend Centre, Blackburn Road, Dunstable, Bedford, England LU5 5BQ). Thus it is known that there is a transient response to the switching of the current, but after a certain time it is considered that the steady state response is reached.
In this conventional approach, the expected time to reach steady state is based on experience, although it is fully understood that the final steady state value is never reached. For practical purposes, however, for this configuration, and within the limitations of the instrumentation and the noise, the steady state value is usually reached after about 0.1 seconds. In some deep low-resolution surveys, where the scale of the setup is increased by an order of magnitude or so, the steady state value may be reached, for practical purposes, only after a few seconds. An example of a measured voltage response to a switch-on current using the dipole-dipole configuration is shown in FIG. 6. This is called the step response. The first part of the response shows an initial step in voltage; in this particular case this is followed by a small dip followed by a rise in voltage that appears to be tending to a steady-state value after about 0.1 s.
FIG. 7 shows the time derivative of the step response of FIG. 6. This is known as the impulse response. The initial large spike in the impulse response corresponds to the initial step in the step response. This is followed by a dip, a rise to a smaller peak, and then a very gradual decrease in amplitude, tending to zero as time increases thereafter. The duration of the impulse response is infinite, just as the duration of the step response is infinite. However, as the amplitude of the impulse response gets smaller and smaller, it becomes harder and harder to measure. When the amplitude is too small to measure, this effectively defines the duration of the transient impulse response.
An object of the present invention is to improve the sensitivity of resistivity measurements of the earth.